Question: William is 2 times as old as Ishaan. 42 years ago, William was 9 times as old as Ishaan. How old is Ishaan now?
Answer: We can use the given information to write down two equations that describe the ages of William and Ishaan. Let William's current age be $w$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $w = 2i$ 42 years ago, William was $w - 42$ years old, and Ishaan was $i - 42$ years old. The information in the second sentence can be expressed in the following equation: $w - 42 = 9(i - 42)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to use our first equation for $w$ and substitute it into our second equation. Our first equation is: $w = 2i$ . Substituting this into our second equation, we get: $2i$ $-$ $42 = 9(i - 42)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $2 i - 42 = 9 i - 378$ Solving for $i$ , we get: $7 i = 336.$ $i = 48$.